This brief appendix is getting ahead of our story a bit, and will not make much sense until you have read certain later portions of this text: in particular, Chapters 5 through 12. I am placing it at this point in the sequence simply because this is where it will be easiest to find when you need to come back to it.
Test for the Significance of the Pearson ProductMoment Correlation Coefficient
If the true correlation between X and Y within the general population is
rho=0 (see Chapter 4), and if the size of the sample,
N, on which an observed value of
r is based is equal to or greater than 6, then the quantity
 t =
 r sqrt[(1—r^{2})/(N—2)]

is distributed approximately as
t (see Chapters 912) with
df=N—2. Application of this formula to any particular observed sample value of
r will accordingly test the null hypothesis (see Chapter 4, et seq.) that the observed value comes from a population in which
rho=0.
To assess the significance of any particular instance of
r,
enter the values of
N[>6] and
r into the designated cells below, then click the 'Calculate' button. (For the distinction between a directional and non directional test, see also Chapter 4, et seq.)